Net Neutrality, Network Capacity, and Innovation at the Edges

Transcription

1 Net Neutrality, Network Capacity, an Innovation at the Eges Jay Pil Choi Doh-Shin Jeon Byung-Cheol Kim May 22, 2015 Abstract We stuy how net neutrality regulations affect a high-banwith content provier(cp) s investment incentives to enhance its quality of services (QoS) in content elivery to en users. We fin that the effects crucially epen on whether the CP s entry ecision is constraine by the Internet service provier (ISP) s network capacity. With limite capacity, prioritize elivery services are complementary to the CP s investments an can facilitate entry of congestion-sensitive content; however, this creates more congestion for other existing content. By contrast, if capacity is relatively large, prioritize services reuce QoS investment as they become substitutes, but improve traffic management. These results are qualitatively robust to the extension of the ISP s enogenous choice of network capacity. JEL coes: D4, K2, L1, L5, O3 Key wors: Net neutrality, network capacity, entry, quality of services (QoS), content provier, queuing, congestion We thank Marc Bourreau, Jane Choi, Ben Hermalin, Jeroen Hinloopen, Joshua Gans, Bruno Jullien, Martin Peitz, Wilfrie San-Zantman, Glenn Woroch, an seminar participants at 2015 AEA meeting at Boston, 2014 EEA-ESEM at Toulouse, 2014 IIOC at Northwestern Univ., 2014 NET Conference at UC Berkeley, 2014 ICT Conference Paris at Telecom ParisTech, 2013 Miwest Economic Theory Conference at Univ. of Michigan, an Georgia Institute of Technology for helpful comments. We gratefully acknowlege financial support from the NET Institute ( through the 2013 summer grant program. An earlier version of this paper was circulate as NET Institute Working Paper #13-24 uner the title Asymmetric Neutrality Regulation an Innovation at the Eges: Fixe vs. Mobile Networks. The usual isclaimer applies. Michigan State University, 220A Marshall-Aams Hall, East Lansing, MI [email protected]. Toulouse School of Economics an CEPR, Manufacture e Tabacs, 21 allees e Brienne Toulouse, France. [email protected]. Corresponing author. School of Economics, Georgia Institute of Technology, 221 Bobby Do Way, Atlanta, GA [email protected]. 1

2 1 Introuction Net neutrality is the principle that all packets on the Internet must be treate equally in their elivery without iscrimination an charges regarless of its content source, estination, an type. The open Internet orer in 2010 represents the U.S. Feeral Communication Commission s (FCC) initial attempt at securing net neutrality, an has serve as a focal guieline for neutrality regulations. 1 However, the FCC s orer has face legal challenges by major ISPs such as Comcast an Verizon Communications. The Unite States Court of Appeals for the District of Columbia Circuit concurre with the ISPs an rule that the FCC oversteppe its authority. 2 In response, on February 26, 2015, the FCC aopte new rules for broaban Internet service by reclassifying high-spee Internet service as a telecommunications service, rather than an information service. 3 This seemingly technical maneuver allows the FCC to circumvent the legal issue of its authority over Internet service an treat the service as a public utility uner Title II of the Telecommunication Act. However, the battle is not yet over, as two lawsuits were file immeiately after the FCC s new rules an more legal challenges to the new regulations are expecte. 4 In this process, the issue of net neutrality has emerge as the most important an controversial regulatory agena since the inception of the Internet. 5 The extant literature on network neutrality has mainly focuse on the expansion of Internet service proviers (ISPs) network capacity as innovation at the core. In this paper, we focus on the implications of neutrality regulation on innovation incentives at the eges to reflect the growing importance of CPs investments in the moern Internet ecosystem. 6 More specifically, the ISPs capacity expansion making bigger pipelines is not the only solution to resolving the congestion problem. In fact, major content proviers such as Google, Netflix, an Amazon have 1 FCC , In the Matter of Preserving the Open Internet, Broaban Inustry Practices (the FCC Orer ), publishe in Fe. Reg. Vol. 76, No. 185, Sept. 23, 2011, went into effect on November 20, See Comcast Corp. v. FCC (600 F.3 642) an Verizon v. FCC (740 F.3 623). 3 FCC 15-24, In the Matter of Protecting an Promoting the Open Internet, release on March 12, See First Lawsuits File Against the F.C.C. s Net Neutrality Rules by Rebecca R. Ruiz in The New York Times on March 23, When the FCC ecie to open up for public ebate regaring new rules for the open Internet, it receive a total of approximately 3.7 million public comments, making net neutrality by far the most-commente issue in agency history. See FCC receive a total of 3.7 million comments on net neutrality by Jacob Kastrenakes in The Verge on September 16, Networks constitute the core of the Internet while content, applications, an evices are at the ege. See Reggiani an Valletti (2012) for more iscussion on this.

3 evelope various measures to improve the quality of service (QoS) for their content an applications, inepenent of the ISP s network infrastructure. For example, they have pursue alternative technological solutions such as content istribution (or elivery) networks (CDN) 7 an avance compression technology to ensure a sufficient quality of service, without asking for preferential treatment of their own content (Xiao, 2008). 8 From an en user s perspective, the funamental goal is to enjoy highest quality of service at a minimum fee; the channel through which this is achieve, either through ISP s capacity investment or CP s CDN investments, is of little interest to en users. Researchers have selom stuie how these new technological changes relate to regulatory ecisions, yet regulators an policy-makers nee to unerstan how the network regulations woul affect the content proviers investments in alternative technology solutions to ensure their quality of services, inepenent of the ISPs (Maxwell an Brenner, 2012). Reflecting technology avances at the eges of the Internet, we evelop a theoretical moel to analyze the effects of net neutrality regulation on innovation incentives of major content proviers. To be consistent with the FCC s interpretation, we characterize neutrality regulation as not allowing for pai prioritization uner which the ISPs can allocate some traffic into a prioritize lane for a premium charge. In this setting, we fin that the effects of net neutrality regulation substantially epens on the relative size of the ISPs network capacity vis-à-vis major content proviers banwith usage. The intuition is as follows. With a limite network capacity, the pai prioritization can facilitate the entry of a congestion-sensitive content provier while the entry may not be mae uner neutral networks because the content provier may fin it too costly to invest up to its esire QoS. For this case, the prioritization complements innovation at the eges. available content woul generate aitional value to the network. content oes not necessarily result in a higher social welfare. The newly However, the entry of new This is because the new content can consume a substantial portion of the existing network capacity, which increases the congestion for other content. Such a negative externality becomes more pronounce with a limite capacity network. Inee, the surplus from new content can be outweighe by the efficiency loss from the 7 CDN is to cache frequently accesse content in various geographical locations, an reirect access request of such content to the closer place. (... ) [B]y moving content closer to en users, CDN can ramatically reuce elay, elay variation, an packet loss ratio for users applications an thus their perception of network QoS (Xiao, 2008 p.117). 8 It is well known that the innovative vieo compression technologies have contribute to better content elivery for live-streaming vieo applications. In aition, thir-party commercial CDN proviers such as Akamai an Internap have rapily expane their businesses to provie a high QoS for content proviers. 2

4 elevate congestion for other content. In contrast, if the network capacity is large enough, prioritize elivery an QoS investment turn into substitutes. Consier a high network capacity case in which the entry of new content is no longer a focal issue. That is, suppose that the high-banwith content proviers enter even without the prioritize service. The prioritization then presents a ifferent trae-off. On the positive sie, the prioritization results in more efficient traffic management by assigning the faster elivery service to the more elay-sensitive content, which is referre to as the traffic management effect. The prioritization thus enhances static efficiency. However, the availability of the prioritize service may ampen content proviers incentives to invest in QoS because the pai prioritization can provie an alternative technological solution to achieve their esire level of QoS. We refer to this uner-investment problem as the QoS investment effect. In other wors, the prioritization may yiel a negative effect on social welfare by weakening ynamic incentives for QoS investment. 9 The social welfare epens on the relative magnitue of these two forces, an we consier it more applicable to the fixe network where the entry of content proviers has not been treate as a serious concern, relative to the mobile network where the network capacity can be a constraint on the entry ecision. We exten the moel to allow for the ISP s investment in network capacity prior to the entry of the major CP. This extension confirms an even strengthens the main insight obtaine for a given capacity. When a major CP s entry critically epens on the ISP s network capacity, the ISP s incentive to inuce entry by investing in capacity is suboptimal regarless of the neutrality regulation regime. Intuitively, this problem is much more severe uner neutral networks in which the ISP s investment incentive is inepenent of the surplus create by the major CP than uner non-neutral networks in which the ISP can internalize the surplus to some egree. Provie that the entry occurs anyway, however, the ISP invests less uner non-neutrality to enhance its bargaining position to such an extent that the major CP fins its entry unprofitable without purchasing a prioritize elivery service from the ISP. By contrast, uner neutral networks the ISP s investment is simply to reuce waiting time for non-major CPs. Overall, these finings suggest that neutrality regulations can be averse to the entry of major CPs when the network capacity is limite an can be a constraint on entry, whereas non-neutrality may reuces the ISP s incentive to invest in 9 Consistent with this insight, Xiao (2008) claims that major content proviers have increase their pursuit of quality of service through technological solutions rather than prioritization after the F.C.C. s intensive efforts to apply network neutrality regulations. 3

5 capacity when the extensive margin is not an issue. This result is consistent with Choi an Kim (2010) who show that the ISP s investment incentives may be weaker uner non-neutral networks in orer to sell the priority at a higher price by making the prioritize service more valuable. As several comprehensive reviews on the literature of net neutrality are available (e.g., Lee an Wu (2009), Schuett (2010), Lee an Hwang (2011), an Krämer, Wiewiorra, an Weinhart (2012)), we briefly provie a selective review of notable works in relation to this paper. The main focus of the extant stuies has been investment incentives for the ISPs on its last mile network capacity. In particular, proponents an opponents of the regulation collie heato-hea on whether the content proviers allege free-riing woul have a chilling effect on the ISPs incentives to upgrae their pipelines. Acaemic research on this issue inclues Musacchio, Schwartz, an Walran (2009), Choi an Kim (2010), Cheng, Banyopahyay an Guo (2011), Economies an Hermalin (2012), Krämer an Wiewiorra (2012), an Njoroge et al. (2013). A relate issue is the content proviers hol-up concern that may result in no entry or less investment in content. This concern arises because investments by high-value content proviers may be expropriate ex post by Internet service proviers who can play as gatekeepers with pai prioritization services. For stuies along this avenue, we refer to Banyopahyay, Guo, an Cheng (2009), Choi an Kim (2010), Grafenhofer (2010), Reggiani an Valletti (2012), an Bourreau, Kourani, an Valletti (2012). We epart from the existing literature on investment incentives by exploring new, but highly important, innovation channels aopte by major content proviers such as Google, Amazon, Microsoft, an Netflix. 10 Beyon investment incentives, economists have stuie how network neutrality woul affect consumer an social welfare from various perspectives, mostly in the framework of two-sie markets. The pricing ynamics of the Internet business have been stuie by Pehnelt (2008), Lee an Wu (2009), Economies an Tåg (2012), an Economies an Hermalin (2012). Several stuies acknowlege the importance of market competition in evaluating the effects of net neutrality. A partial list inclues Becker, Carlton, an Sier (2010) an Bourreau et al. (2012) who focus on the competition between ISPs on the consumer sie, whereas Mialon an Banerjee (2013) are more concerne with the market structure of the content sie. Hermalin an Katz (2007) analyze the 10 From an en user s perspective the goal is to enjoy the highest quality of service at a minimum fee. In this regar, it oes little matter how this goal is achieve, either through the ISP s capacity investments or CPs CDN investments. Inee, there seems to be a consensus on the basic premise that en-users quality of service must be the primary goal of a esirable network ecosystem (Xiao (2008), Altman et al. (2012), an Guo, Cheng, an Banyopahyay (2013)). 4

6 effects of network neutrality on consumer an social surplus by viewing neutrality regulations as a prouct line restriction in vertically ifferentiate prouct space. Taking a similar approach, Choi, Jeon, an Kim (2015) evelop a moel of secon-egree price iscrimination in a two-sie market to stuy how the business moels of content proviers affect social welfare with an without the regulation. As common in the literature, we also aopt the two-sie market approach with a monopoly platform; however, we focus on positive externality from CPs investments in alleviating network congestion an negative externality from new CPs entry to an alreay congestive network, an investigate how the interplay of such externalities affects consumer an social welfare. In this regar, Peitz an Schuett (2015) is closely relate to our paper. They consier so-calle congestion control techniques that ecrease packet losses uring elivery to users with an inflation of traffic by sening multiple reunant packets. This practice may be privately optimal but aggravates the congestion problem on the network. They introuce the tragey of common property resources into the net neutrality iscussion an show that net neutrality regulation may lea to socially inefficient inflation of traffic whereas the socially optimal allocation can be achieve with tiere pricing. In contrast, our paper investigates the effects of net neutrality regulation on CPs investment incentives in CDN or compression technologies, which ecreases the packet size of iniviual content an generates a positive spillover to the network. Consiering the importance of innovations at the eges of the Internet, it seems very important to offer formal analyses to unerstan CPs innovation incentives an the resulting externalities associate with such innovations. We also fin Economies an Hermalin (2015) relate to this paper. Offering a new explanation for why ISPs offer plans with ownloa caps, they show that congestion externality can inuce ISPs to use ownloa limits as a mechanism to restrict the aggregate banwith usage. 11 Both moels eal with quality ecisions by CPs an aress how congestion externalities affect social welfare, but through ifferent channels. The remainer of our paper is organize as follows. We present our moel in Section 2 incluing a generalize queuing moel which escribes how prioritization an CPs investment affects congestion. In Section 3, we first show that the first-best outcome is characterize by iscrimination across content types with ifferent sensitivities to elay. This implies that net 11 Recently, irect payments from consumers to content proviers have receive more attention by researchers. Gans (2015) an Economies an Hermalin (2015) consier a setting in which consumers nee to pay content-specific prices to content proviers, whereas Choi et al.(2015) consier micropayments in a reuce form represente as CPs business moels. 5

7 neutrality regulation can be justifie only as a secon-best policy when a social planner cannot irectly control content proviers entry an investment ecisions. Then, we analyze the QoS investment ecisions by the major content proviers uner neutral an non-neutral network regimes. In Section 6, we analyze the ISP s enogenous choice of network capacity an its impact on our finings from the preceing analysis. Section 7 presents some extensions of our moel. We consier heterogeneous consumers, a iscontinuous QoS in congestion, an multiple major CPs. We wrap up with concluing remarks in Section 8. 2 The Moel 2.1 ISP, CPs, an Consumers We consier a monopolistic broaban Internet service provier (ISP) who is in charge of last mile elivery of online content to en-users. 12 Since we are primarily intereste in major content proviers inepenent investment incentives to improve quality of service, we consier two types of content proviers: one major content provier (henceforth, simply referre to as MCP ) such as Google, Netflix, Disney, an Amazon Instant Vieo, an a continuum of other non-major content proviers (simply, NCPs ) whose mass is normalize to one. This istinction allows us to focus on MCP s investment ecision to improve QoS for a successful content business; the MCP s relatively large scale of operation justifies the costly investment. There is a continuum of homogeneous consumers whose mass is normalize to one. Let v an V enote the consumer s intrinsic utility from consuming MCP s content an NCPs respectively. Each consumer experiences a isutility from elays of content elivery ue to network congestion. We aopt an aitive utility specification in which the net surplus ecreases in the average waiting time for both types of content, respectively enote by w an W. Then, a consumer earns the gross utility: u(w) = v kw U(W ) = V W for MCP for NCPs where k 1 measures the relative sensitivity of MCP s content to elays compare to NCPs of which sensitivity is normalize to one. Normalizing the mass of consumers to one, u(w) an U(W ) 12 In reality, the Internet is a network of networks with multiple network service proviers. It is not uncommon that an originating ISP may not be the same as a terminating ISP for complete elivery of content, with several interconnecte network proviers being involve along a transit route. Choi et al. (2015) aresses an equivalence in the choice of network qualities between interconnecte ISPs an a monopoly ISP. (1) 6

8 also represent the entire surplus from each type of content. We assume MCP can extract the entire surplus u(w) by charging consumers for elivere content in the absence of a priority service uner net neutrality, but it negotiates with the ISP over the price of the priority service in a non-neutral network. 13 For NCPs content, we introuce a parameter β [0, 1] to enote the ISP s share of the total surplus generate by NCPs content elivery. In other wors, the ISP receives βu(w ) from proviing elivery services for NCPs content; the rest of the surplus, (1 β)u(w ), is share among NCPs an en users. The parameter β can be seen as the ISP s ability to extract rent from NCPs an en users via connection fees. Alternatively, one may regar β as a measure of the extent to which the ISP internalizes any externality inflicte on NCPs an en users by its ecisions. If β = 0, the ISP will not take into account any potential effects on NCPs content traffic when the ISP eals with MCP. By contrast, if β = 1, the ISP will fully internalize the externality. As will be clearer later, the parameter β plays an important role in assessing the welfare effects of net neutrality regulations. The private an the social planner s incentives coincie when β = 1 because the ISP fully internalizes any externality create in its ealing with MCP. However, for any β < 1, there may be a iscrepancy between the ISP s optimal ecision an the social planner s, with the potential for iscrepancy more pronounce with a lower β. 2.2 Network Congestion, CP s Investment an QoS Improvement Users initiate the Internet traffic through their clicks on esire content an become final consumers of the elivere content. As a micro-founation to moel network congestion, we aopt the stanar M/M/1 queuing system which is consiere a goo approximation to congestion in real computer networks. 14 Let µ enote the ISP s network capacity. Each consumer emans a wie range of content from both MCP an NCPs. The content request rate follows a Poisson process, which represents the intensity of content eman. For NCPs content, we normalize the arrival rate of the Poisson istribution an the size of packets for each content to one. Since the mass of the NCP is one, the overall eman parameter (i.e., the total volume of traffic) for NCPs content is also normalize to one. By contrast, we envision MCP as one iscrete player operating a content network platform 13 In Section 7.1, we relax the assumption of full rent extraction by the MCP an show that this simplification oes not change our results qualitatively. 14 Choi an Kim (2010), Cheong et al. (2011), Bourreau et al. (2012), Krämer an Wiewiorra (2012) aopt the M/M/1 queuing moel to analyze network congestion. 7

9 that provies a continuum of content whose aggregate packet size is given by λ. Then, we can interpret λ as the sheer volume of MCP s content or a measure of the relative traffic volume of MCP s content vis-à-vis NCPs aggregate traffic volume. 15 The total traffic volume for the ISP thus amounts to 1 + λ an we nee the conition of µ > 1 + λ for a meaningful analysis of network congestion; otherwise, the waiting time becomes infinity. The MCP can make an investment of h 0 to enhance the quality of service in its content elivery. As iscusse earlier, the investment can take various forms, such as compression technology to reuce packet-size or content elivery networks (CDN) that shorten the elivery istance by installing content servers at local ata centers so that en-users emans are serve by the closest ata center. 16 The common objective of all such investments is to spee up content elivery to enhance the user experience. We thus moel them simply as an investment in a compression technology that woul reuce the traffic volume of the major CP s content from λ to aλ, where a = 1 1+h (0, 1]; more investment leas to a smaller packet size for MCP s content. Therefore, its elivery spee increases even without the ISP s capacity expansion. No investment (h = 0) correspons to a = 1. We assume the investment cost is increasing an convex in the investment level, i.e., c (h) > 0 an c (h) > 0, an satisfies the Inaa conition of c(0) = 0 an c (0) = 0 with a fixe cost of operation F > 0 upon entry. We consier two network regimes: neutral an non-neutral networks. Consistent with the literature an regulatory obligations, we take the availability of a pai prioritize service as the efining characteristic that istinguishes the two network regimes. In the neutral regime, there is no pai prioritization: all traffic is treate equally with every packet being serve accoring to the best-effort principle on a first come, first serve basis. In the non-neutral regime, ISPs are allowe to provie a two-tiere service with the pai priority class packets elivere first. In the neutral network, both MCP s an NCPs content are elivere with the same spee. More specifically, each user in the M/M/1 queuing system faces the following total waiting time 15 For instance, if MCP s content mass is ξ an the packet size for each content is m, then we have λ = ξ m. 16 Accoring to Xiao (2008), there are at large three ifferent types of elays that account for the total elay from one en of the network to the other: (1) en-point elay, (2) propagation elay, an (3) link (or access) elay. Increasing spee of bottleneck links can be the most effective approach to aress (3), whereas caching or content elivery networks (CDN) helps to reuce (2). The ISP s capacity expansion at the last mile helps to reuce (1). While the total elay is collectively affecte by all these ifferent types of elays, en-users typically cannot istinguish what type of elay affecte their perceive quality of service. 8

10 for the major CP s content: w n (a, µ) = 1 µ (1 + aλ) } {{ } waiting time per packet aλ }{{}. total packet size (2) The total volume of traffic (packet size) amounts to 1+aλ (one for NCPs content an aλ for MCP s content with compression 17 ), an thus the average waiting time per packet is given by 1 µ (1+aλ) for both types of content. With the packet size of aλ for the major CP s content, the total waiting time is compute as (2). With no investment in the compression technology (h = 0, or a = 1), the average waiting time reuces to 1 µ (1+λ) the non-major CP s content, we can erive the total waiting time as W n (a, µ) = because the total packet size for NCPs content is one. as in the stanar M/M/1 queuing system. Similarly, for 1 1. (3) µ (1 + aλ) Without neutrality obligations, the ISP may aopt a pai prioritization in which MCP can purchase the premium service at some price to sen its content ahea of NCPs packets in queue so that the waiting time for the prioritize packets is given by w (a, µ) = 1 aλ. (4) µ aλ The faster elivery of the prioritize packets is achieve at the expense of NCPs content. Once the priority service is introuce, the non-prioritize content is elivere at a slower spee; the waiting time for the basic service in the non-neutral network is given by W (a, µ) = µ 1 1. (5) µ (1 + aλ) µ aλ In what follows, when there is no confusion, we often suppress the epenence of a on h with w r (h, µ) = w r (a(h), µ) an W r (h, µ) = W r (a(h), µ), where r = n,. 17 Strictly speaking, queuing happens at the package level but compression at ata-level so that the packet size is ifferent from the packet quantity. However, here we use them interchangeably because simple normalization can make this conversion possible. Specifically, let λ = a DMCP MT U where D MCP enotes the average ata intensity of MCP an MTU stans for the maximum transmission unit. If we normalize the MTU an the average ata intensity of NCPs both to one, our notations make the two concepts interchangeable. 9

11 2.3 Generalize Queuing System an Its Properties Using (3)-(6), we can erive the following set of properties that are not only intuitive but also serve collectively as an important micro-founation for our analysis. Property 1 The major content provier s investment to enhance its own quality of service generates positive spillover into other content in both neutral an non-neutral networks: i.e., W n h < 0 an W h < 0. Intuitively, less use of banwith from one content provier means more network capacity for other content in a given network capacity. Property 2 For a given pair of (a, µ), the prioritization makes the waiting time for prioritize major CP s content shorter, an the waiting time for non-major content longer than the respective ones in the neutral network: i.e., w (a, µ) < w n (a, µ) an W (a, µ) > W n (a, µ). Property 3 regimes: i.e., For a given pair of (a, µ), the total waiting time is equal regarless of the network w n (a, µ) + W n (a, µ) = w (a, µ) + W (a, µ). This result is an extene version of the waiting cost equivalence characterize in Choi an Kim (2010), Bourreau et al. (2012), Krämer an Wiewiorra (2012) in a more generalize queuing system that allows for a content provier s investment for QoS enhancement an its spillover effects. Intuitively, the total waiting time must epen on the network capacity an the total packet size to be elivere whether or not a subset of the packets is prioritize. Property 4 For a given pair of (a, µ), prioritizing the major CP s traffic reuces the total elay cost: i.e., kw n (a, µ) + W n (a, µ) > kw (a, µ) + W (a, µ) for any k > 1. This is because the major CP s content is assume to be more sensitive to congestion (k > 1) an the prioritization allocates more congestion-sensitive content to the faster lane. Formally, this property is prove by applying Properties 2 an 3: [kw n (a, µ) + W n (a, µ)] [kw (a, µ) + W (a, µ)] = (k 1)[w n (a, µ) w (a, µ)] > 0. 10

12 2.4 Decision an Bargaining Timings In the neutral network, MCP s ecisions are straightforwar since it oes not involve a bargaining situation with the ISP. N-1. For a given ISP s network capacity µ, the major CP makes a ecision on whether to enter the market. If MCP enters, it chooses its investment level h. N-2. For a given (µ, h), content is elivere to consumers an the payoffs are accoringly realize. In the non-neutral network, we nee an aitional stage in which the major CP an the ISP bargain over the price of the prioritize service. D-1. For a given µ, the CP an the ISP bargain over the price of the prioritize service. D-2. With an agreement on the price of the prioritize service, MCP makes its entry an investment ecisions taking the prioritize service into account. Without a mutual agreement, the prioritize service is not introuce an, as in the neutral regime, all traffic is elivere without any preferential treatment uner the best effort principle. The MCP s entry an investment ecisions remain the same as in the neutral regime. D-3. Given (µ, h) an a priority class, content is elivere to consumers an the payoffs are realize. We assume MCP s investment is not contractible in that the MCP an the ISP can agree only on the priority price, but the investment ecision is solely left to MCP. 3 Optimal QoS Investment an Network Regimes 3.1 Benchmark: The First-best We first characterize the first-best outcome (given a network capacity µ) in which the social planner can control MCP s entry an QoS investment ecisions as well as the network regime. In our setup, the comparison of alternative network regimes is meaningful only when MCP s entry is relevant. If there is no entry, the etermination of the network regime in the first-best outcome is vacuous because there is only one type of content provier. We thus focus on the case in which the social planner inuces the entry of MCP. Denote the socially optimal QoS investment level in each network regime by h F B r for r = n, that is characterize as follows: h F B r = arg min h r Ψ r (h) = kw r (h) + W r (h) + c(h). (6) 11

13 Then, we can establish the following intuitive result. Proposition 1 (First-Best Comparison) Suppose that the social planner inuces the entry of the major CP. Then, for k > 1, the first-best non-neutral network is always superior in welfare to the first-best neutral network. Proof. See the Appenix. Proposition 1 tells us that the first-best outcome always entails a non-neutral network when MCP s entry is socially esirable because it allows a more efficient traffic management compare to a neutral network (Property 4). This result suggests that net neutrality regulation can be justifie only as a secon-best policy when the entry an the investment ecisions are left to the private parties. In fact, our subsequent analysis reveals that a secon-best neutral network can provie a higher social welfare than a secon-best non-neutral network. 3.2 Neutral Networks Consier a neutral network in which all packets are equally treate base on the first-come-firstserve principle. As usual, we procee with backwar inuction an istinguish two subgames epening on whether or not MCP has entere. Assuming MCP s entry, the content provier s optimal choice of h is to maximize its profit: where w n (h, µ) = λ (µ 1)(1+h) λ π n h max h 0 π n = v kw n (h, µ) c(h) F, from (2). The first-orer conition with respect to h becomes = h n kλ(µ 1) [(µ 1)(1 + h) λ] 2 c (h) = 0, (7) for an interior solution h n. The marginal benefit of the investment ecreases in the ISP s network ) capacity, which is easily confirme by the cross-partial erivative < 0. Let π n (µ) π n (h n(µ), µ) enote the maximize profit of MCP at the optimal investment level h n(µ) for a given network capacity µ. By the Envelope Theorem, we fin the MCP obtains a higher profit as the network capacity increases: πn µ = π n µ = k w n(h n, µ) µ µ ( πn h λ(1 + h = k n) [(µ 1)(1 + h > 0. (8) n) λ] 2 This relationship implies that a threshol network capacity µ n exists such that π n(µ) 0 if an only if µ µ n. In other wors, MCP makes an investment only when the ISP s capacity is above 12

14 Figure 1: Optimal QoS Investment in the Neutral Network this threshol level. For a sufficiently low capacity µ < µ n, the investment cost is too high to justify entry into the content service market. Hence, there is a iscontinuity in MCP s investment at the threshol value µ n : no investment for µ < µ n but h n > 0 for µ µ n. Furthermore, we analyze how the (interior) optimal investment h n changes with the capacity level for µ > µ n an establish the following lemma: Lemma 1 The MCP s QoS investment ecreases in the ISP s network capacity µ, i.e., h n µ < 0 for µ µ n. Proof. See the Appenix. We can illustrate the optimal QoS investment in the neutral network as in Figure 1: h n = 0 for µ < µ n an then h n > 0 an h n µ < 0 for µ µ n. 3.3 Non-neutral Networks Now consier a non-neutral network in which MCP has an option to buy a prioritize elivery service at a negotiate price. One benefit of such an arrangement is that MCP can achieve the same quality of service with a lower investment in the compression technology ue to a preferential treatment of its content elivery. The analysis for the non-neutral network procees similarly as in the neutral network. Suppose that MCP an ISP agree on a price of the prioritize service. We efine MCP s profit gross of any payout for the priority as π u kw (h, µ) c(h) F, (9) 13

15 where w (h, µ) = λ µ(1+h) λ. The first-orer conition for MCP s optimal investment ecision with the prioritize service (h ) yiels the following equation: π h = h kλµ [µ(1 + h) λ] 2 c (h) = 0. (10) Defining π (µ) π (h (µ), µ), we can show that the maximize profit increases in the network capacity, i.e., π µ = π µ = k w (h, µ) µ λ(1 + h) = k [µ(1 + h) λ] 2 > 0, an the optimal investment ecreases in the capacity, h µ < 0.18 While the investment ecision h is inepenent of β, the price of prioritization must be affecte by the level of β because the pai prioritization will make the ISP earn less from NCPs content ue to increase elay for non-prioritize content. The ISP woul ask for compensation from MCP for the loss via the priority price. The ISP s incentive to provie the prioritize service woul be higher as β becomes smaller. In this section, we analyze the case of β = 0, in which MCP s entry is facilitate to the maximum extent, an relegate the analysis of β > 0 to the next section. 19 In particular, if β = 0, the ISP an the major content provier will agree on some price of prioritization whenever π (µ) > 0. As MCP s profit π (µ) strictly increases with µ as in the neutral network, there will be another threshol capacity µ such that π (µ) 0 if an only if µ µ. Again, MCP s investment iscretely jumps up at the threshol µ, then ecreases with µ for µ > µ. Because π (µ) > π n(µ) an π (µ) increases in µ, we must have µ n > µ. The last step neee to compare h n an h is to verify that the marginal benefit of the QoS investment is greater in the neutral network compare to that in the non-neutral network. The reason is that the marginal benefit from reucing the content elivery size increases with the severity of congestion in the network, as is shown below. π n h > π h because we have w n(h) = Consequently, we establish the following lemma: λ(µ 1) [(µ 1)(1 + h) λ] 2 > λµ [µ(1 + h) λ] 2 = w (h). Lemma 2 The major CP reuces its QoS investment with the purchase of the prioritization service, i.e., h n(µ) > h (µ), for all µ > µ n. 18 The proof is omitte as it is similar to the process leaing to Lemma 1 in Section We formally erive this result in the next section (see Lemma 5). 14

16 3.4 Network Capacity an QoS Investments Base on Lemmas 1-2, we can summarize the major CP s optimal investment ecisions for β = 0 in the following Proposition. Proposition 2 Suppose β = 0. (i) For a limite network capacity of µ [µ, µ n ), a pai prioritization an MCP s investment are complements in that prioritization inuces MCP to enter an make a positive investment, whereas the major CP oes not enter in the neutral network. (ii) For a larger capacity µ > µ n, prioritization an MCP s investment are substitutes in that purchasing prioritization reuces the major CP s QoS investment, compare to the investment that woul be mae in the neutral network. We illustrate the optimal QoS investments in both network regimes in Figure 2. The upwar arrow for the range of µ < µ < µ n epicts the greater QoS investment uner the non-neutral network compare to the neutral network. The ownwar arrow when µ > µ n shows the smaller investment with the pai prioritization. Intuitively, the prioritization reuces the QoS investment incentives because it provies an alternative technological solution to achieve the esire level of QoS. Figure 2: Optimal QoS investments, Net Neutrality, an Network Capacity Our analysis shows that MCP s entry crucially epens on the ISP s network capacity. In the remainer of the paper, we refer the limite capacity case of µ (µ, µ n ) to as extensive margin 15

17 case an the high capacity case of µ > µ n to as intensive margin case in the sense that MCP s entry is a focal issue in the former but not in the latter. 4 The Extensive Margin Case In this section let us analyze the effects of net neutrality regulation on various participants when MCP makes no entry uner the neutral regime because πn(µ) < 0 for µ < µ n but the entry becomes possible in the non-neutral network (at least for β = 0). 4.1 Effects of MCP s Entry on Congestion Uner a non-neutral network, MCP s entry has two countervailing effects. On one han, the new content generates a positive surplus π (µ) > 0, which can be share by the content provier an the ISP accoring to their respective bargaining powers. On the other han, the entry exacerbates the network congestion through following two channels: The aitional banwith taken by the new MCP s content means more congestion for a given network capacity. In aition, the prioritize elivery of MCP s content means a slower elivery for NCPs content. Formally, we examine the ifference in waiting time for the non-major CPs content with the introuction of a two-tiere service, W, that can be ecompose into two parts. W W (h (µ), µ) W n(φ, µ) = [W n (h (µ), µ) W n(φ, µ)] + [W } {{ } (h (µ), µ) W n(h (µ), µ)], } {{ } (+) ue to new content entry (+) ue to ifferent priority classes (11) where φ stans for no entry of the MCP. The first brackete term in (11) measures the increase in elivery time even in the absence of prioritization ue to increase traffic volume with the entry of the major CP the Internet pipe now nees to be share with the major CP. The secon one captures the non-major content s waiting time increase ue to the prioritization for a given QoS investment h. On both accounts, NCPs suffer from longer elivery time, i.e., W > 0. We confirm this intuition formally by showing that W = a [ λ (2µ a λ 1) µ (1 + a λ) ] (µ a λ) (µ 1) > 0 for any a (0, 1]. 4.2 Effects of Prioritization on the ISP an Social Welfare We now examine the ISP s incentives to provie the prioritize service in the non-neutral regime an the overall welfare effects of this prioritization. The prioritize service will be provie to MCP 16

18 an its price will be agree upon between the ISP an MCP if their joint profits increase with the service. The joint profits uner the neutral regime will be given by Π n (φ, µ, β) = β[v W n (φ, µ)] because there is no entry in the neutral network. With a priority service in the non-neutral network, their joint profits are given by Π (h, µ, β) = π (h, µ) + β[v W (h, µ)]. The change in joint profits ue to introuction of the prioritization can be written as follows: 20 Π E (µ, β) Π (h (µ), µ, β) Π n(φ, µ, β) = π (µ) β W (µ), (12) where the superscript E in Π E enotes that we consier the case that the MCP s entry (extensive margin) generates the key trae-offs. As (12) clearly shows, the MCP s entry generates the value of π (µ) but the ISP must bear the loss of β W (µ) ue to its negative effects on NCPs. Recalling Π m (µ, β = 1) equals to the change in social welfare from the MCP s entry, one can immeiately see that any private incentives to introuce a prioritize service uner β < 1 excees the socially optimal incentives. Specifically, the iscrepancy between the private an social incentives is measure by (1 β) W (µ), which is inversely relate to β. If β = 1, the ISP completely internalizes the effects on consumers an NCPs, with the private an social incentives coinciing. Recognizing the crucial role of the network capacity in measuring the effects of a prioritization on social welfare an private incentives to introuce it, we examine how Π E (µ, β) changes with µ for a given β. First, we analyze the effects of a marginal change in network capacity on the waiting time for MCP s content in the non-neutral network (w ) as follows: w (h (µ), µ) µ = w (h (µ), µ) µ + w (h (µ), µ) h h µ. (13) A small increase in µ has a irect positive effect on the quality of service, represente by the first term on the RHS in (13). However, an inirect negative effect counteracts: the MCP respons to a higher network capacity by reucing its QoS investment. We fin that the positive irect effect ominates the negative inirect effect. Lemma 3 The waiting time in the non-neutral network unambiguously ecreases as the network (µ), µ) capacity increases regarless of priority classes: (i) w (h (µ), µ) µ < 0 an (ii) W (h µ < 0. Proof. See the Appenix. From (12) an Lemma 3-(i), it is clear that Π E (µ, β) strictly increases in µ if β = 0 for 20 Note that W oes not epen on β because h is inepenent of β. 17

19 any k 1; by continuity, this result hols for a small β. Even if β is not that small, the private incentives to introuce a prioritization still increases with µ if the elay sensitivity parameter for the MCP s content, measure by k, is sufficiently large. Lemma 4 There exists k(µ, β) such that for k k(µ, β), Π m (µ, β) strictly increases in µ. Proof. See the Appenix. The intuition for Lemma 4 is simple. As k increases, the social benefit of being able to assign a fast lane to MCP s content also increases while the negative effect of the entry on NCPs content remains constant. Because the ISP takes only a part of the negative externality into account, if β is small enough, the ISP will fin it better to offer the prioritization an the MCP will make the entry even when k is very close to one. We efine µ (β) as the cutoff capacity above which MCP enters. 21 The MCP s investment h (µ) is inepenent of the parameter β given its entry an W is also a constant regarless of the egree of β, the joint profits of the ISP an MCP conitional on MCP s entry strictly ecreases with β for a given µ. Lemma 5 summarizes this result: Lemma 5 Suppose k k(µ, β). Then, µ (β) strictly increases with β. Any entry uner µ < µ (1) is socially harmful; Lemma 5 tells us that such an excessive entry can occur for any β < 1. This is because the coalition of the ISP an MCP oes not fully internalize the negative externality of increase congestion onto the non-major content. Using Lemmas 4-5, we obtain the following Proposition. Proposition 3 Consier the extensive margin case with µ [µ, µ n ). Suppose k k(µ, β). (i) Given a β, a pai prioritization inuces MCP s entry as long as µ µ (β), where µ (β) strictly increases with β starting from µ (0) = µ. (ii) If µ (1) < µ n, MCP enters in a non-neutral network though the entry is not socially esirable for µ (µ (β), µ (1)). By contrast, the entry is socially efficient for µ (µ (1), µ n ) an the prioritization makes this socially esirable entry possible. 22 Figure 3 illustrates Proposition 2-(ii): when µ (1) < µ n, MCP makes a socially inefficient entry ue to the pai prioritization for the shae range of µ. Remarkably, the socially excessive 21 With this notation, we confirm that the cutoff capacity efine for β = 0 in Section 3 is expresse as µ (0) = µ. 22 If µ n < µ (1), there is no socially efficient entry ue to the prioritization. 18

20 Figure 3: Social Efficiency an Private Entry Decision entry is not an eventual outcome all the time; in Section 7.1 we show an insufficient entry can arise if one consiers consumer heterogeneity an/or competition between ISPs. 5 The Intensive Margin Case In this section we consier a network in which the network capacity is large enough to inuce the major content provier s entry regarless of the network regimes, i.e., µ µ n. In other wors, now the MCP s content is available without a prioritize service. Recall that the joint payoffs of the ISP an MCP are given in the network regime r = n, as follows: Π r (h, µ, β) = π r (h, µ) + β[v W r (h, µ)] (14) where n stans for neutral networks an for non-neutral (iscriminatory) networks. Hence, the prioritization will be aopte if the two parties fin the non-neutral regime better than the neutral treatment: i.e., Π I (µ, β) = Π (h (µ), µ, β) Π n(h n (µ), µ, β) > 0, (15) where the superscript I inicates that we are consiering the intensive margin case an Π I (µ, β) > 0 means a higher joint payoff uner the non-neutral network. For the intensive margin case, we fin a ifferent trae-off that we escribe below from the trae-off reporte for the extensive margin case. 5.1 A New Trae-off: Traffic Management vs. Uner-investment The effects of the prioritization on the joint payoff can be ecompose into two parts: (1) static traffic management effect an (2) ynamic QoS investment effect. Formally, it yiels that Π I (µ, β) = [Π (h (µ), µ, β) Π n(h (µ), µ, β)] + [Π } {{ } n (h (µ), µ, β) Π n(h n (µ), µ, β)]. (16) } {{ } Traffic Management Effect (+) QoS Investment Effect ( ) 19

21 The first term in (16) is always positive an we refer it to as the traffic management effect : for a given QoS investment level h, prioritizing the MCP s traffic reuces the total elay cost because MCP s content is more sensitive to congestion (k > 1). Precisely, we have Traffic Management Effect = Π (h (µ), µ, β) Π n(h (µ), µ, β) (17) = k[w n (h (µ)) w (h (µ))] + β [W n(h (µ)) W (h (µ))] = k[w n (h (µ)) w (h (µ))] β [w n(h (µ)) w (h (µ))] = (k β)[w n (h ) w (h )] > 0 where the thir equality in (17) is obtaine from Property 3, w n (h )+W n(h ) = w (h )+W (h ).23 The inequality is clear because k > 1 β an Property 2, w n (h ) > w (h ). We refer the secon square bracket in (16) to as the QoS investment effect : the availability of a prioritize service will ecrease the MCP s investment level from h n (µ) to h (µ) (Lemma 2), which in turn affects the resulting joint payoff. To etermine the sign of this term, let h J n (µ, β) enote the MCP s investment choice that maximizes the joint profit of the two parties in the neutral regime, i.e., h J n (β) = arg max h which is alternatively efine as Π n (h, µ, β) = π n (h, µ) + β[u W n (h, µ)] (18) h J n (β) = arg min h kw n (h) + c(h) + βw n (h). (19) From the profit maximization problem (18), we can see that the MCP s private optimal choice, h n(µ) that maximizes π n (h, µ), fail to incorporate its positive externality on the NCPs content. The joint ecision on the QoS investment internalize such externality only part of it, βw n (h). Thus, the joint ecision yiels so-calle uner-investment problem. This logic can be earne from the cost minimization problem (19) in which MCP chooses h n(µ) to minimize kw n (h)+c(h), but ignores the aitional cost βw n (h). In sum, in either interpretation, we fin that a uner-investment problem persists in that h n(µ) < h J n (µ, β) for any β > 0. This result combine with Lemma 2, h (µ) < 23 The traffic management effect can be erive irectly from Property 4 when consumer utility an ISP s profit are specifie as linear functions in the waiting costs an the QoS investment is evaluate at h. 20

22 h n(µ), 24 proves that the uner-investment problem is more serious in the non-neutral network compare to the neutral network: formally, it means the QoS investment effect must be negative: QoS Investment Effect = Π n (h (µ), µ, β) Π n(h n (µ), µ, β) < 0. (20) 5.2 Effects of Prioritization on Social Welfare We now analyze a social planner s incentive to introuce the pai prioritization an compare it with the private incentive. We consier the constraine (secon-best) social optimum in which the social planner can choose the network regime only, but the QoS investment is left to the MCP s ecision. The social welfare in each regime coincies with the joint payoff of the ISP an MCP when β = 1 for (14), which is given by S r (µ) = Π r (h r(µ), µ, β = 1) = π r (h r(µ), µ) + [U W r (h, µ)], (21) where r = n,. Let S(µ) be the effect of the prioritization service on social welfare: S(µ) = S (µ) S n (µ) = Π I (µ, β) + (1 β) [W n (h n) W (h )] (22) As is clearly seen, if β = 1, the private incentive to aopt the prioritization service is perfectly aligne with the social incentive (i.e., S(µ) = Π I (µ, 1)). For any uninternalize externality with β < 1, however, we have socially excessive aoption of the pai prioritization as the ISP an MCP woul not fully internalize the effect of increase elay on NCPs content which is represente by S(µ) Π f (µ, β) = (1 β) [W n (h n) W (h )] } {{ } externality on NCP s content We can further ecompose the externality term in (23) an show S(µ) < Π f (µ, β) as follows: (23) W n (h n) W (h ) = [W n(h n) W n (h )] + [W n(h ) W (h )] < 0 (24) The first term of (24) has a negative sign because of Lemma 2 (h n > h ), an the secon term also takes a negative value following Property 2. Lastly, we notice that the iscrepancy between 24 Note that the objective function [kw n (h) + βw n (h)] + c(h) in the minimization problem is a convex function of h because each component of w n (h), W n (h), an c(h) is also convex in h. The convexity of the objective function warrants the clear comparison. 21

23 the social incentives an the private incentives is inversely relate to β. Interestingly, we fin that if the iscrepancy reaches its maximum (β = 0), the ISP an MCP will always fin it profitable to aopt the prioritization in the non-neutral network regarless of whether the neutrality regulation woul give higher social welfare. To see this, we verify the following: Π I (µ, β = 0) = π (h (µ), µ) π n(h n (µ), µ) (25) π (h n(µ), µ) π n (h n (µ), µ) = w n (h n(µ), µ) w (h n (µ), µ) > 0, where the first (weak) inequality comes from the reveale preference argument an the last inequality from Property 2. case. Proposition 4 summarizes thus far finings for the intensive margin Proposition 4 Consier a network with µ > µ n in which MCP always enters. Then, we fin (i) A prioritization service involves a trae-off between the positive efficient traffic management effect an the negative QoS investment effect. (ii) A prioritization will be aopte only when the gain from the better traffic management excees the loss from the iminishe QoS investment. (iii) If β is close to zero, the ISP an MCP always fin the prioritization profitable in the nonneutral networks. (iv) In general, there exist socially excessive incentives to aopt a prioritization service, i.e., S(µ) Π I (µ, β). 5.3 Net Neutrality as a Secon-Best Policy We close this section by offering a numerical example that illustrates net neutrality regulation as a secon-best policy. Accoring to Proposition 1, in the first-best worl, non-neutrality yiels the higher welfare than neutrality because of the traffic management effect (there is no QoS investment effect in the first-best). However, as the below example shows, this is no longer the case in the secon-best worl because the uner-investment problem is more severe in a non-neutral network than in a neutral network. For explicit erivations, let us consier a cost function of c(h) = h 2 an set the values of parameters µ = 3, λ = 2, u = 5, U = 3, an F = 0 for k {1, 2, 3}. Table 1 shows the contrast between the first-best an the secon-best outcomes. 22

24 Table 1: First-Best vs. Secon-Best k h n h h F B n h F B S S n S F B Sn F B The comparison between optimal QoS investments shows that the uner-investment problems occur in both network regimes (i.e., h F B n is larger in the non-neutral network (h F B > h n, h F B h > hf B n because the quality of service can be enhance through prioritization. > h ), but the extent of the uner-investment h n) where MCP reuces its investment When one consiers the symmetric waiting cost, i.e., k = 1, the first-best outcomes are the same in both network regimes (S F B = S F B n ). For the secon-best, the neutral network is better (S < S n) because of the less severe uner-investment problem in the neutral network an zero efficiency gains from traffic management by prioritization. For a moest asymmetry in the congestion costs (k = 2), the non-neutral network outperforms the neutral network for the first-best (S F B > Sn F B ) because the efficiency gain via the better traffic management gives rise to a higher first-best welfare in the non-neutral network (Proposition 1). However, the opposite hols for the secon-best (S < S n): the more severe negative effect of the uner-investment problem in the non-neutral network outweighs the positive traffic management effect (Proposition 4). If k is sufficiently large (k = 3), such conflict isappears. Now the non-neutral network starts to give higher social welfare both in the first-best an secon-best sense because the traffic management effect ominates the QoS investment effect even in the secon-best outcome. The potential necessity of net neutrality regulations as a secon-best policy is reminiscent of Choi et al.(2015). While our fining soun similar, the logic iffers. In our earlier work, we show that a menu of multiple qualities may yiel an excessive quality istortion for the basic service such that the resulting social welfare is even lower in the non-neutral network compare to in the neutral network. Here, this possibility comes from the substitution between the QoS investment an the prioritization available only uner the non-neutral network. 6 ISP s Capacity Choice In our baseline moel, we focuse on MCP s QoS investment for a given ISP s network capacity. Because it is very important to unerstan potential interplays between the ISP s capacity choice an the MCP s entry/investment ecisions, here we augment our moel to inclue a new initial 23

25 stage when the ISP ecies µ prior to the MCP s actions. Precisely, at the new initial stage N-0 or D-0, the ISP chooses its network capacity before all subsequent plays ensue. Let C(µ) enote the investment cost of capacity µ with C > 0 an C > 0. For analytic simplicity an clarity, we aopt two assumptions for this section. First, although we know that the waiting time w r (h r(µ), µ) an W r (h r(µ), µ) epen on µ both irectly an inirectly through h r/ µ, we conuct our analysis by assuming that the inirect effect is of a secon-orer to the irect effect, which shoul hol if c(h) is convex enough. Secon, we assume v an k are large enough to capture a situation in which the QoS of the high-banwith content is crucial to consumer utility. Both assumptions are not restrictive for main results. As a benchmark case, consier the ISP s optimal capacity choice in the absence of MCP, which is characterize by β W n(φ, µ) µ = C (µ). (26) The LHS measures the marginal benefit from a small increase in the capacity, which is the reuce waiting time for the NCPs content. the RHS captures the marginal cost. Let µ φ n(β) be the solution to (26). 6.1 Neutral networks The ISP s optimal capacity in a neutral network must epen on whether the ISP inuces the MCP to enter or not. If the ISP inuces the entry an MCP chooses h n(µ), the optimal capacity is etermine by [ Wn (h β n(µ), µ) µ + W n(h n(µ), µ) h h ] n = C (µ). (27) µ Let µ E n (β) be the solution to (27). Let us consier a hypothetical situation where MCP enters but choose zero investment (i.e., h = 0), an enote the ISP s optimal capacity µ E n (β) in this scenario. Then, µ E n (β) will satisfy β W n(0, µ) µ = C (µ). Intuitively, the MCP s QoS an the ISP s capacity investment become substitutes as the ISP woul invest less when MCP can make a positive investment compare to when MCP cannot (i.e., h = 0). To verify this intuition, we compare the marginal benefit of MCP s capacity expansion uner h n(µ) with that with h = 0. Then, we can confirm µ E n (β) < µ E n (β) from the inequality of [ Wn (h β n(µ), µ) µ + W n(h n(µ), µ) h h ] n µ < β W n(0, µ), µ 24

26 because the irect effect β Wn(h n(µ),µ) µ ecreases with h an the inirect effect is also negative from Wn(h n (µ),µ) h < 0 an h n µ < 0. Recall that µ n enotes the minimum level of the network capacity to inuce the MCP s entry in a neutral network. Thus, a necessary conition for the ISP to inuce MCP s entry requires µ n < µ E n (β). Otherwise, the ISP only nee to invest µ n to inuce the MCP s entry, but this strategy woul give a lower profit to the ISP compare to inucing no entry by choosing µ n ε, where ε > 0 is infinitesimal. This is because the entry of MCP woul only increase congestion to the NCPs content as is seen from W n (φ, µ n ) < W n (h n(µ n ), µ n ). In general, no entry can occur with either µ = µ n when µ n < µ φ n(β) or µ = µ φ n(β) when µ φ n(β) < µ n. So, we use the minimum operator min{µ φ n, µ n } for the capacity inucing no entry. Obviously, the ISP woul inuce entry if an only if it yiels more profit than no entry, i.e., βw n (φ, min{µ φ n, µ n }) C(min{µ φ n, µ n }) βw n (h n(µ E n ), µ E n ) C(µ E n ), (28) which is equivalently given as C(µ E n ) C(min{µ φ n, µ n }) β[w n (φ, min{µ φ n, µ n }) W n (h n(µ E n ), µ E n )]. (29) Inequality (29) hols if the cost of capacity expansion is sufficiently cheap an β is sufficiently large. Given that the ISP chooses either min{µ φ n, µ n } or µ E n, welfare is higher with MCP s entry if an only if W n (φ, min{µ φ n, µ n }) C(min{µ φ n, µ n }) π n (h n(µ E n ), µ E n ) W n (h n(µ E n ), µ E n ) C(µ E n ), (30) where π n (h n(µ), µ) > 0 always hols since µ E n (β) > µ n. By comparing (28) an (30) using C(µ E n ) > C(min{µ φ n, µ n }) from µ E n > min{µ φ n, µ n }, we fin MCP s entry is socially esirable whenever the ISP inuces entry. However, the converse is not always true. A socially esirable entry can be blocke by the ISP since it oes not take into account MCP s profit. Also, the ISP s capacity choice in a neutral network is always suboptimal when it inuces MCP s entry, because the ISP ignores the effect of its investment on w n (h n(µ), µ). 6.2 Non-neutral Networks Now let us examine a non-neutral network in which the ISP an MCP bargain over the price of prioritization, so that without the neutrality regulation, the ISP s investment ecision epens on its bargaining power against MCP an its efault payoff if the bargaining fails. We assume the Nash 25

27 bargaining with equal bargaining power between the two. Because of ifferences in efault payoffs, we shoul istinguish two cases epening on whether or not MCP enters without prioritization. Consier the first case in which MCP oes not enter without prioritization an the efault payoffs follow no entry payoffs. objective: Then, the ISP chooses its capacity to maximize the following {π (h (µ), µ) β [W (h (µ), µ) W n(φ, µ)]} 2 + β [U W n (φ, µ)] C(µ). (31) The first term in (31) is the half of the surplus create by prioritization, an the secon term is the ISP s efault payoff. The first-orer conition with respect to µ is given by k 2 w (h (µ), µ) β µ 2 W (h (µ), µ) β W n (φ, µ) = C (µ). (32) µ 2 µ Let µ(β) enote the solution to Equation (32). For the case of no entry, the ISP s capacity must be constraine by the upper-boun µ n, which means the optimal capacity (conitional on no entry { without prioritization) is µ E (β) = min µ(β), µ n }. 25 Consier the secon case in which MCP enters even without prioritization. Then, the ISP s objective is given by {π (h (µ), µ) π n(h n(µ), µ) β [W (h (µ), µ) W n(h n(µ), µ)]} 2 The first-orer conition with respect to µ is given by k 2 [ w (h (µ), µ) w n(h ] n(µ), µ) β µ µ 2 + β [U W n (h n(µ), µ)] C(µ). (33) W (h (µ), µ) β W n (h n(µ), µ) = C (µ). (34) µ 2 µ When k is large enough, the LHS of (34) is preominantly etermine by the brackete term. In aition, since we assume the inirect effect through the change in h r( ) is of a secon-orer compare to the irect effect, the brackete term is by an large etermine by w (h (µ), µ) w n(h n(µ), µ) µ µ a = ( (µ)λ µ a (µ)λ ) 2 + a n(µ)λ (µ 1 a n(µ)λ) 2 > 0 where a 1 r(µ) = 1+h. Hence, if k is large enough an c( ) is convex enough, the LHS of (34) r(µ) takes on a negative value: the ISP has no incentive to invest. This implies that the constraint that 25 A necessary conition for the ISP to inuce MCP s entry with prioritization is µ E (β) > µ (β). 26

28 MCP enters without prioritization (i.e., µ µ n ) bins. Therefore, our analysis shows that the ISP invests µ n, conitional on inucing entry of the MCP. The ISP wants to maximize the surplus create by its prioritization service, which is mainly riven by the ifference in the waiting time, k[w n (h n(µ), µ) w (h (µ), µ)] for a sufficiently large k. A marginal capacity investment is more effective in reucing w n than w, which in turn ecreases the surplus create by prioritization. This is why the ISP wants to minimize its investment; a similar effect was obtaine by Choi an Kim (2010). Given that MCP only enters with prioritization, we can show that the ISP never chooses a capacity level that allows MCP s entry without prioritization. Suppose to the contrary that the ISP chooses µ n. Then, comparing (31) an (33) reveals that the ISP s profit is higher when entry is not allowe in the absence of prioritization because W n (φ, µ) < W n (h n(µ), µ). 26 in favor of the ISP an assume MCP oes not enter without prioritization given µ n. 27 We break ties We now examine the ISP s incentive to inuce MCP s entry with prioritization in a non-neutral network. Following similar analysis applie to the neutral network, we fin that the ISP chooses min{µ φ n, µ } if the ISP oes not inuce entry, but µ E (β) if the ISP inuces entry. Thus, the ISP will inuce entry if an only if βw n (φ, min{µ φ n, µ }) C(min{µ φ n, µ }) { π (h (µe ), µe ) β [ W (h (µe ), µe ) W n(φ, µ E )]} βw n (φ, µ E 2 ) C(µE ). (35) As is shown in the RHS of (35), the ISP internalizes a half of the surplus create by entry, π (h (µe ), µe ) in the non-neutral network. By contrast, such a rent oes not show in the RHS of (28) in the neutral network. This implies that non-neutrality incentivizes the ISP to make investments to facilitate the MCP s entry. Given that the ISP chooses either min{µ φ n, µ } or µ E (β), welfare is higher with entry if an only if W n (φ, min{µ φ n, µ }) C(min{µ φ n, µ }) π (h (µe ), µe ) W (h (µe ), µe ) C(µE ), (36) Comparing (35) with (36), we can see that the entry bias can operate in either irection. The 26 Here we use π n (h n(µ), µ) = 0 at µ = µ n. 27 For example, the ISP can choose µ n ε with an infinitesimal ε > 0 to inuce no entry. This argument shows that when entry occurs with prioritization, the ISP chooses µ E (β) an inuces no entry without prioritization. 27

29 ISP can capture only a half of the surplus create by entry, which inuces insufficient entry. In contrast, the negative externality on NCPs content arises ue to MCP s entry in a non-neutral network, which is not fully internalize by the ISP, implying an excessive entry. However, if we assume π (h (µe ), µe ) is sufficiently large compare to the effects on NCPs content elivery time ue to MCP s entry (which trivially hols when k an v are large enough), then whenever the ISP oes inuce entry, it is also socially esirable. But, socially esirable entry is blocke by the ISP if (35) hols but (36) oes not. Proposition 5 summarize our finings in this section. Proposition 5 Consier the ISP s investment problem before the MCP s entry. Assume that v an k are large enough an that c( ) is convex enough. (i) (Incentives to inuce the entry) Regarless of the neutrality regulation, the ISP s incentives to inuce the entry of MCP is lower than the social incentives. This problem is more severe in a neutral network than in a non-neutral network in which the ISP partially internalizes the surplus create by the entry. (ii) (Investment incentives when MCP enters in equilibrium) In the neutral network, the ISP invests µ E n (β) where µ E n (β) > µ n. The ISP invests to reuce the waiting time for NCPs. The ISP s investment is lower by expecting the MCP s subsequent QoS investment compare to the MCP s commitment to zero QoS investment. In the non-neutral network, the ISP invests µ E (β) where µe (β) µ n an inuces MCP not to enter without prioritization. The ISP s investment is optimally limite because the larger capacity woul ecrease the ISP s extraction of the surplus create by inucing the entry via prioritization. The result in Proposition 5-(ii) is reminiscent of Choi an Kim (2010): a iscriminatory network may not warrant a higher investment of the ISP since a lower congestion woul mean a eclining value of a prioritize service. In a neutral network, however, there is another kin of concern: the incentives to inuce entry is lower than in a non-neutral network. Overall, Proposition 5 suggests that when a network capacity is limite, the neutrality regulation can be averse to the entry of major content proviers, whereas when the entry is not an issue, non-neutrality may reuce the ISP s incentive to invest in capacity. Therefore, we fin the extene moel with the ISP s capacity investment provies consistent implications with those in our baseline moel. 28

30 7 Extensions 7.1 Consumer Heterogeneity In our baseline moel, we consiere homogeneous consumers an full surplus extraction by MCP from its content elivery. 28 In such a setting, consumers always suffer from entry of MCP s highbanwith content ue to the negative externality on the existing NCPs content for any β < 1. This simplification is innocuous to the results that we have erive, for we have focuse on social welfare. However, for a more realistic analysis of consumer welfare an its implications for net neutrality regulations, we nee to exten our moel such that some consumers enjoy a certain positive surplus from MCP s content elivery. For this spirit, let us introuce consumer valuation heterogeneity in the simplest way: two types of consumers, H with proportion γ (0, 1) an L with 1 γ. 29 The utility level that a type i {H, L} consumer erives from MCP s content in the neutral network will equal to u i (w n ) = v i kw n an in the non-neutral network to u i (w ) = v i kw. Let δ = v H v L > 0. Furthermore, assume that MCP prefers to serve both types than to serve only H-type. 30 In such a case, L-type consumers only suffer from MCP s entry, whereas now H-type consumers earns a surplus of δ from the new content though they still suffer from the elevate congestion for the existing NCPs content. Then, the social welfare comparison in the non-neutral network will be etermine by the trae-off between π an W = [W (h (µ); µ) W n(φ; µ)], where π = π γδ an π is MCP s profit from full surplus extraction. Our previous analysis in Section 4 remains qualitatively intact by replacing π with π. Remarkably, with consumer heterogeneity, we fin that the MCP s entry can be socially insufficient. This result provies a nuance contrast to Proposition 3-(ii) that we focuse on the excessive MCP s entry. Specifically, a prioritization will be introuce only if Π E (µ, β) Π (h (µ), µ, β) Π n(φ, µ, β) = π (µ) γδ β W (µ) > 0, (37) but the entry will be socially inefficient if Π E (µ, β) µ=µ (1) < 0. If the conition γδ+β W (µ) µ=µ (1) > W (µ) µ=µ (1) (i.e., W (µ (1)) < γδ 1 β ) hols, then a socially optimal entry oes not take place. 28 We i not specify how the rent was extracte. One can think of micro-payments such as pay-per-view, membership fees, an/or various types of online avertising. 29 One caveat is that one may introuce heterogeneity of consumers by assuming a uniform istribution over u i an erive a linear eman. But, it woul unnecessarily complicate the analysis without further insight to be gaine. 30 This woul be the case if v L is sufficiently large compare to δ an/or γ is relatively small. 29

31 This implies that the concern for socially excessive entry is mitigate an we may have insufficient entry when MCP cannot extract the entire consumer surplus Discrete QoS in Congestion We have consiere a consumer s utility is a continuous function in the congestion level. However, it is not necessarily the case for some real-worl applications. For example, a consumer who is watching a movie through a vieo streaming platform such as Netflix may stop subscribing to the service when he or she fins the content elivery unsatisfactory ue to frequent buffering or a blurry screen. A user woul not value a Voice over Internet Protocol (VoIP) when calls rop too often or the call quality is below a certain level, whereas the same user may feel inifferent once the QoS is above a certain level. Accoringly, we coul consier the utility function as the following step function, u(w) = { u 0 for w w o w > w o while the non-major content is assume to have no iscontinuity in the QoS. One avantage of working with a iscrete QoS function is to be able to erive explicit solutions for QoS investments. In the neutral network with a sufficiently large capacity µ, there will be no nee for any investment from MCP to warrant its minimum quality requirement. The upper-boun capacity, enote by µ n, can be erive from w n (h = 0) = λ µ (1+λ) = w 0 as follows: µ n = 1 + λ + λ w o. The MCP s optimal investment to ensure the require QoS, enote by h n, is erive from w n (h n ) = λ (µ 1)(1+h n) λ = w o: h n(µ) = 1 + w o w o λ µ 1 1 for µ < µ n. (38) In the non-neutral network, MCP can have an option to buy the prioritize elivery service at a certain price. The benefit of such an arrangement is that the investment level that ensures the require common QoS for the content can be lowere compare to in the neutral network. Solving w (h = 0) = λ µ(1+h) λ = w o, we can erive the threshol capacity above which no investment is 31 In the same spirit with consumer heterogeneity, suppose that a competition between MCPs plays a role of reucing MCPs payoffs. Then, even without consumer heterogeneity, an insufficient entry of major content proviers is possible. We leave explicit moeling MCPs competition for further research. 30

32 require to ensure the require QoS in the non-neutral network: µ = λ + λ w o. There will thus be two cases epening on the range of network capacity. For µ µ, the purchase of the priority leas to no extra investment: that is, h = 0. By contrast, for µ < µ the major content provier woul nee an aitional investment of h (µ) = 1 + w o w o λ µ 1 for µ < µ. (39) From the optimal QoS investments explicitly erive in (38) an (39), we can replicate most of qualitative results that we have thus far obtaine. However, two ifferences are noteworthy when we use this specification of a iscrete quality of service. First, the purchase of the prioritize elivery class becomes a complete substitute for the QoS investment when µ > µ. That is, MCP will make no investment with the prioritize elivery service, which is not the case for a continuous utility function in QoS as in (1). Secon an more important, in a iscrete QoS utility setting the traffic management effect is no longer guarantee to be positive. For instance, consier (a, µ) such that w n (a, µ) w o. Then, prioritizing MCP s content has no effect on its effective waiting cost, but only increases the waiting cost for NCPs content, implying a negative traffic management effect. 7.3 Multiple MCPs One may woner how much our moel of a single MCP woul restrict economic insights compare to multiple MCPs. For iscussion s sake, let us consier two MCPs but all logic can be applie generally for any N 2. With multiple MCPs, there are at least three new factors to be involve. First of all, heterogeneous MCPs may have ifferent entry conitions so that each may or may not enter the network without the priority. Secon, we nee to istinguish the two ifferent situations: (i) the ISP sells the prioritize service to one of the two MCPs exclusively (Choi an Kim, 2010) or (ii) the ISP sells it to both at the same time (Cheng et al, 2011). Thir, the entry an resulting payoffs are affecte by whether the two MCPs are competing entities (if so, how intensive the competition is) or not. One s exclusive priority can imply one s competitive avantage over the other when the two are competing, which is similar to an instrument of raising rival s cost which may block the potential competitor s entry. Thus, even with the two MCPs there are many subcases to be examine an three factors can interplay intricately. Here let us iscuss economic 31

33 insights to be gaine in this extene moel, leaving etaile analysis a future research agena. Suppose the network capacity is sufficiently large so that two MCPs can provie their own content without entry concern. From social welfare perspective, the neutrality regulation involves the same trae-off characterize in Section 5 for the internal margin case between static traffic management an ynamic QoS investment. If the ISP allocates the fast-lane to only one MCP, the ifference between the payoffs with an those without it will etermine the winner an the transfer price will epen on bargaining powers. The competition between the MCPs will make the exclusive priority more valuable an thus yiels more rent to the ISP. If the ISP elivers the priority to both MCPs, the relative value of the priority ecreases compare to the exclusive priority. While these new factors woul generate more nuance results, we fin that our key insight is robust to this extension. Now suppose the capacity is small an each MCP nees a prioritize service (regarless of its exclusiveness) for effective content business. In this external margin case, from the viewpoint of the social welfare, we woul again obtain the same trae-off feature in Section 4 between new content an congestion externality. With the exclusive priority, the new content effect is limite but congestion externality is also refraine. Again the value of the priority is expecte to be higher with more intense competition among MCPs. Overall, we fin our moel oes not lose the main economic forces. However, some interesting issues may arise with multiple MCPs. For example, suppose that MCPs are heterogeneous in their costs of QoS investment an only highly efficient MCP(s) can enter without the prioritization, but less efficient MCPs can enter the network only with the prioritize service. Woul the social welfare be higher in a non-neutral network than in a neutral network? We think that it crucially epens on how the efficient MCPs (whose entry is unrestricte) woul respon to new entrants in a non-neutral network. The new entrants increases the overall traffic volume so that the incumbents nee to invest more on their QoS investments to eliver the content successfully, which generate positive externality. Interestingly, the extent of the new entry will be enogenously affecte by the incumbents investments. Since non-major CPs will be also affecte by the changes in QoS investments an the congestion externality, an social welfare varies with new content entry, more elicate analysis is require to sort out various interactions. So, we acknowlege a moel of multiple MCPs offers more nuance results as well as new research agena, but our simple moel maneuvers to eliver key economic insights with substantial tractability. 32

34 8 Conclusion The ebate on net neutrality has been the most important an controversial regulatory agena since the inception of the Internet. 32 Not surprisingly, economists have extensively stuie an helpe to frame various issues, e.g., effects of network neutrality regulations on ISPs investment incentives an on consumer surplus an social welfare, as well as on the entry/exit of content proviers. Yet, the extant literature have not pai ue attention to its effects on another crucial innovations taking place at the eges of the Internet in reality, although it is imperative for scholars, regulators an policy-makers to grasp how network regulations woul affect these innovations at the eges (Maxwell an Brenner, 2012). In this paper, we evelop a theoretical moel that characterizes the relative size of network capacity as a istinguishing feature to allow the entry of a congestion-sensitive content, an investigate major content proviers incentives to invest in QoS. Our analysis shes new light on various trae-offs that net neutrality regulations bring forth to social welfare. The pai prioritization service can inuce high-banwith content proviers to enter the limite capacity mobile networks with greater QoS investments, but this comes at the cost of increasing total traffic volume. When the entry is not constraine by the network capacity, the prioritization relieves content proviers of their buren of QoS investments an improves efficiency by allocating the higher spee lane to more congestion-sensitive content. However, smaller QoS investments may be etrimental to social welfare. Our insight is consistent or even strengthene when we consier the ISP s incentive to invest in capacity. We hope that our analysis benefits the on-going neutrality ebate. 32 As of May 6, 2015 net neutrality gives 1.28 million search results at news.google.com an 14.2 million Google web results, which inicates how net neutrality has become newsworthy in a short perio. 33

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37 Appenix: Proofs Proof of Proposition 1 The proof is straightforwar as the following inequalities establish: Ψ (h F B ) = kw (h F B < kw n (h F n B ) + W (h F B ) + W n (h F B n ) + c(h F B ) + c(h F B n ) kw (h F B n ) = Ψ n (h F B n ) ) + W (h F n B ) + c(h F n B ) The first line of the above proof is by a reveale preference argument. The secon inequality is base on Property 4. Proof of Lemma 1 For the comparative statics, let us efine an implicit function G(h n ; µ, k, λ) kλ(µ 1) [(µ 1)(1+h n) λ] 2 c (h n ) = 0 from (7) aroun the point h n. Then, we can apply the Implicit Function Theorem as follows: G h n µ µ = (h n) G hn=h n h n (h n). Once can easily etermine the signs of the enominator an the numerator of hn µ hn=h n: G h n (h n) = 2kλ(µ 1) 2 [(µ 1)(1 + h n) λ] 3 c (h n) < 0; which proves Lemma 1. G µ (h n) = kλ(µ 1)(1 + h n) kλ 2 [(µ 1)(1 + h n) λ] 3 < 0, Proof of Lemma 3 Proof of Part (i) Our reasoning follows proof by contraiction. Let µ be an initial capacity an µ (> µ ) a new capacity. Suppose, as a working hypothesis, in negation that w (h (µ ), µ ) < w (h (µ ), µ ). Then, let h be efine as w (h (µ ), µ ) = w (h, µ ), (40) which is equivalent to λ µ (1 + h (µ )) λ = λ µ (1 + h ) λ. (41) Note that µ > µ combine with (40) means h < h (µ ). In aition, w (h (µ ), µ ) < w (h (µ ), µ ) implies that the major content provier woul invest less than h when µ = µ. From the first-orer conition for h ( ), we know h (µ ) must satisfy the following conition: λµ k [ µ (1 + h (µ )) λ ] 2 = C (h (µ )). (42) The marginal gain of investment for the major CP with h = h at µ = µ can be expresse as the following equivalent equations: λµ k [µ (1 + h ) λ] 2 = k λµ [ µ (1 + h (µ )) λ ] 2 = C (h (µ )) µ µ. 36

38 The first equality hols because of (41), an the secon one is from (42). From h < h (µ ), however, we must have C (h (µ )) µ µ > C (h ). Hence, at the choice of h = h at µ = µ, the marginal gain excees the marginal cost. contraicts the working hypothesis of w (h (µ ), µ ) < w (h (µ ), µ ). Proof of Part (ii) Using the result of Part (i), we can state that This w (h (µ), µ) µ = w (h (µ), µ) + w (h (µ), µ) h µ h µ = w (a (µ), µ) + w (a (µ), µ) a µ h µ [ ] a = ( λ µ a λ ) 2 + λ ( µ a λ ) + a ( λ2 µ a λ ) 2 a µ < 0 The last inequality is equivalent to Now, we use the waiting cost for the non-major content of a µ < a µ. (43) W (a (µ), µ) = µ µ (1 + a λ) 1 µ a λ an show the following two inequalities: [ ] µ µ (1+a (µ)λ) µ < 0 an [ ] 1 µ a (µ)λ µ < 0. Regaring the first inequality, we have [ ] µ µ (1+a (µ)λ) 1 = µ µ (1 + a λ) µ [ µ (1 + a λ) ] 2 + λ µ [ µ (1 + a λ) ] a 2 µ, which becomes negative if Using (43), we show that inequality (44) always hols. Similarly, regaring the secon inequality, we show that [ ] 1 µ a (µ)λ 1 = ( µ µ a λ ) 2 + λ ( µ a λ ) 2 a µ < 1 + a λ = 1 λµ λµ + a µ. (44) a µ < 0 if a µ < 1 λ, 37

39 which also hols from (43) as µ > aλ. Because both prouct terms in W (a (µ), µ) ecrease in µ, the proof of Part (ii) is complete. Proof of Lemma 4 The total erivative of Π m (µ, β) with respect to µ yiels Π m (µ, β) µ = π (µ) β [W (h (µ), µ) W n(φ, µ)] = k w µ µ µ β W µ β W n µ > k w µ β W n µ = k a λ (µ a β 1 λ)2 (µ 1) 2, (45) where in the first inequality we use Lemma 3(ii), i.e., W µ < 0. A sufficient conition for Πm (µ, β) to increase in µ can be characterize by k k(µ, β), where k(µ, β) = β a λ ( µ a ) λ 2, (46) µ 1 that is, Π(µ,β) µ 0 an the equality hols at k = k. k k The right-han sie of inequality (46) is ecreasing in a λ. In particular, if a λ > 1, the threshol k is smaller than one, regarless of k 1 an β [0, 1]. Intuitively, if the traffic volume of the high-banwith content is so large (a λ > 1), the relative merit of the non-neutral treatment is always increasing in the capacity. 38